PLEASE HELP! supply me with answers and work
1. in triangle ABC, a=3, b=5, c=7. What is m<C?
2. if tan A= (2/3) and sin B=(5/√41) and angles A and B are in Quadrant 1, find the value of tan(A+B).
3. if sin A=(2/3) where 0 degrees < A< 90 degrees, what is the value of sin2A?
4. In triangle ABC, m<A=32, a=12, and b=10. Find the measures of the missing angles and side of triangle ABC. Round each measure to the nearest tenth.
1. I will be using Heron's formula for finding the area of triangle, then use that to find the missing angle.
On the other hand `A=1/2*a*b*sinC => 6.50=1/2*3*5*sinC =>`
So angle C measures 60.
2. We will be using the fact that `tan(A+B)=(tanA+tan B)/(1-tanA*TanB)`
Using the pythagorean theorem we can find that `tanB=5/4`
3.Here I will be using `sin2A=2sinAcosA`
Knowing that sine=opposite/hypotenuse, we can use the pythagorean theorem to find the adjacent side, hence the cosine.
Thus measure of sin2A=`(4sqrt(5))/9`